ICinetics of Sucrose Crystallization J
PURE SUCROSE SOLUTIONS ANDREW VAN HOOK Lafayette College, Easton, Pa. The enhanced velocity .of crystallization of sucrose from This simple order is the one UGH work has been pure aqueous solutions at high supersaturations may be indicated by the results of reported on the rates accounted for on the basis of the increased activity of of crystallization of the majority of workers, and sucrose in solution. The fundamental rate equation is: sucrose from pure and impure on this basis typical results at 30’ C. for the adjustment solutions. Sugar refining velocity = k (a amsu.) of seeded sugar solutions are proceases operate under the The activities are estimated by rather long but reasonable shown in Figure 1. These relatter. condition, and the time extrapolations of vapor pressure data. Published and new sults were obtained at a stirfactor in such a case is vastly data on velocity of growth, even in the presence of proring speed of 400r.p.m. with a different from that underideal nounced false grain, can be accounted for by this means. propeller type blade of diamconditions of high purity. Nevertheless it is imperative eter just less than that of the containing vessel. T o emphasize the effects of added seed and to to have a satisfactory description of the kinetics in pure solutions before a successful understanding of the actual working process adjust conditions to convenient experimental observation, most of the experiments reported were performed at an initial supercan be expected. The complete course of crystallization consists of the consaturation of aboiit 1.15, which is considerably above the usual working range for sugar crystallization. At this high supersecutive processes of nuclei generation and the subsequent growth of these nuclei. I n ordinary commercial practice the operation saturation but without added seeds, a considerable turbidity deof the first factor is subdued by “graining”. However a t high velops during the time of an ordinary run, yet the total amount of crystallized sucrose is not detected refractometrically. The supersaturation, high temperature, and rapid agitation, seed curves presented thus represent principally the crystallization generation is manifest as “false grain” which will operate to augment the observed rate of crystallization (31). on added seed and false grain developed, as distinguished from spontaneously generated nuclei. A seed to sirup.ratio of 1 to RELATIVE CRYSTALLIZATION VELOCITY 20, of 40-60 mesh seeds, was used, Larger amounts of this standTwo general methods of investigating the kinetics of the ard size seed, or’equal amounts of smaller size seed, shortens and crystallization of pure sucrose are available: (a) the direct evaluaeventually eliminates the induction period with a simultaneous tion of the growth velocity by direct measurement of individual increase in the slope of the major curve. This behavior imcrystals suspended in excess of sirup, and (a) the change in conmediately relates the observed induction period with an areacentration of sirup in which a large number of seed crystals are producing mechanism. Consistent results above coefficients growing. The second method is the more convenient of the two, of 1.20 were not abtained and therefore are not included in the yet i t is not generally utilized for the determination of the abanalysis. Close adherence to a standardized procedure was necessary to obtain duplicate results, especially in the presence solute velocity of crystallization since i t has not been possible of ammonium and the trivalent metal salts. Inversion and carto estimate with certainty the large surface of the growing crysamelization effects were minimized by heating the solution only tals. Since comparative results were the primary interest of this sufficiently to form the sirup and then cooling immediately. work, the second method was used, as described in detail by Whittier and Gould (97). The refractive index of strong sirups is The acidity of all the sirups examined except a t extremely high approximately linear in terms of the supersaturation coefficient, salt concentrations did not differ from that of a corresponding pure sucrose solution. % sucrose in sirup The general features of these curves are an initial slow rate of % sucrose in satd. sirup ED a(n na) 4adjustment which is emphasized as an induction period (or even where n, n, refractive a slight peak), the higher indicea of sirup and saM. the original supersaturasirup, respectively tion, followed by a unimolecular section exand thus may be subtending from about one stituted dizectly in place quarter t o more t h a n of in the integrated three quarters of the form of the monomomaximum amount of lecular growth equation; crystallizable sucrose, Le., and then a section invelocity dicating lagging velocity. k (c e-) with = The linearity is extended c/c- gwes: by using supersaturation in terms of sucrose t o 1 so-1 water ratios in place of k = ;log d 10 15 20 211 30 s-1 the usual Coefficients, Time,minutes but for the present dis1 m-nm Figure 1. Monomolecularity of Sucrose Crystallization at Differ-jlog cussion theimprovement ent Supersaturations (30’ C., 400 R.P.M., 1/10 of 40-60 Mesh Seeds) n - ?&m
M
-
-
-
- -cdc/d2 =i
-
1042
INDUSTRIAL A N D ENGINEERING CHEMISTRY
November, 1944
is not necesaary. Over not too large a concentration range the two modes of expressing concentration are proportional t o one another. The factors responsible for the deviating parts of the curve are considered t o be:
EARLYSECTION
1. Establishment of a large and effectively constant seed area,
principal1 by disinte ration 2. . Nomsot~ermalconiitions due t o evolved heat of crystallization 3. Enhanced solubility of small grains
LATESECTION
Slowly decreasing area available for crystallization due to accretion and aging or perfecting of crystals 5. Diminishing crystallizing activlty of sucrose
4.
Undoubtedly other explanations are poeaible and may operate. Of those suggested, factor 1 is considered most determinative in the early part of the curve and factor 4 in the later part, with factor 5 becoming more significant with the more concentrated solutions.
1.0
6
1s
Time, Minutes
1043
as being quite different in nature and extent from the well aged and developed crystal (18). This interpretation that false grain is principally the disintegration and erosion fragments of the added seed is supported by observations on the effects of rate of stirring on the velocity curves. I n general, maximum and minimum rates of crystallization are attained with increasing or decreasing rates of stirring in the same equipment. With a given initial supersaturation the induction period is retained although it becomes less certain a t lower rates of stirring. These results Rre represented schematically in Figure 2, where 85 r.p.m. was the slowest practical speed for the stirrer used. Below this speed the crystals were not evenly suspended in the sirup, and very erratic results were obtained because of this nonuniformity. However with an e x c w (1/15) of fin& seed (xxxx), good results may be obtained by allowing crystallization to occur dire&ly in the smear on the refractometer prism. This is a reasonable technique according t o the subsequent discussion, and in view of greater convenience much of the later data was obtained in this way. Suspension of the coarser seed by a reciprocating sieve gave approximately the same limiting value. Between these limiting values the relation of velocity constant to stirring speed is roughly linear.
20
Figure 2. Effect of Stirring S eed on Crystalliaation Speed Sucrose (SO l.lb:30° C., '/moof 40-60 Mesh Seeds) A. '/u of
xxxx
B. 400 and
& r.p.m.
meed.
direotly on refractometer ri.m
C.
250r.p.m.
D. 150r.p.m. E. Piston F. 85r.p.m.
FACTOR 1. The little that is known regarding nucleation of sugar sirups may be summarized by Webre's criteria (36) that spontaneous crystallization occurs above a coefficient (weight per cent) of 1.07-1.08,whereas only added seeds will grow below 1.03-1.06. I n between is a region of false grain, in which added seeds beget more seeds. I n this work these criteria were confirmed, in the main, for gently stirred sirups using well developed and consolidated seeds over relatively short periods of time. (Surface dust is eliminated from dry seed by suspending in a saturated sirup and superheating 10-20' for a short time, 82). If stirring is more violent or if the observation time is sufficiently long, spontaneous nucleation inevitably occurs, even in sirups a t very low coefficient. False graining seems to become more pronounced the higher the supersaturation, the greater the number of seeds (glass beads substitute effectively), and the more violent the stirring (11,38). Microscopically the growth of individual crystals in oversaturated sirups is irregular and not uniform. Nodules form which may be swept off if agitation is sufficient and thus give rise to new centers of crystallization. This action is accompanied by sluffing off of corners and edges. The subsequent perfection of sucrose crystals is a slow process which takes place at concentrations close t o saturation. The actioq is emphasized with unconsolidated but well-graded seed crystals. Undoubtedly the incipient fractures of the previous processing enhance the stresses and strains of the solution Ft crystallization forces involved in the nonuniform growth of added nuclei. This mechanism conforms with the current concept of crystallization and precipitation, which regards the initially formed and fresh surface
1.0
k/kso
-
1.16
2.0
Figure 3. Velocity Constant us. Initial Supersaturation at 30' C. This work (column 5. Table I). t Amagaaa (1). unoomtad, larue 0x06.. area
of meed.
Since the velocity of crystallization may not be limited by a diffusional mechanism even at slow rates of stirring, as will be shown later, the upper critical stirring speed suggests a marked and severe shattering action of the stirring mechanism itself; the lower limit (if real) and the persistence of the induction period suggest that this erosion process is assisted (perhaps preceded) by a disintegration of the crystal lattice upon immersion in the supersaturated sirups. The persistence of the lagging period of crystallization a t low initial concentration and high rates of stirring (Figure 1) are in agreement with this sbggestion. The effects of low stirring rates a t low initial concentrations are too uncertain t o separate these two factors. It is also observed that sugar crystals can be disintegrated by agitating in saturated sirup even a t low rates. Likewise the seed count a t lOOX of a reaction, SO = 1.16, just after the induction period is approximately the same as if is near the end of this same reaction end,
Vol. 36, No. 11
INDUSTRIAL AND ENGINEERING CHEMISTRY
where the primes indicate supersaturation coefficients in terms of the more significant sugar/ water ratios rather than the previous unprimed weight percentages, and y is the activity coefficient of sucrose in aqueoue solution. Then
Wsing values of y presented later in this report, the values of k’ given in column 7 (Table I) were computed. The spread of values between So = 1.06 and 1.2 is in the ratio of 1/2, which is just about the observed total nuclei (added plus developed) densitx ratio. At a low rate of stirring, approximately unit value is observed for the ratio of seed densities O.?# while the ratio of computed k 0.1 0.01 0 0.01 values has dropped to 1/1.2 (S’ - I), grams sugar/100 g. water (S - l), weight per cent This substantiates the suggewFigure 4. Kucharenko’s Values ( 1 3 ) for Velocity us. Supersaturation tion that the extent of false-, graining depends on both agitation and supersaturation, but more extensively on the former within a factor of 2, is the same in number (but not size) for a run Column 9 gives values of k’ computed from experiments in whick of smaller initial supersaturation. This suggests that mechana large excess of very fine seed was used. The area-produring ical action of the stirrer is most significant in establishing the factors are apparently obscured in the results. area of crystal growth. Analytically the above equation approximates a t not too high On the basis of these suggestions we may eliminate the area supersaturations to a linear dependencd of the velocity constant correction term throughout a given reaction, since a n effectively on the supersaturation. This is borne out in Figure 3 with large and constant area is being generated during the induction Amagasa’s data ( 1 ) and a t low concentrations with thc present period in each case. This conclusion is confirmed by area cordata. Since Amagasa does not specify the amount of seed ernrection calculations on data of the type of Figure 1, when no subployed in his experiments, it is not possible to compare these r e stantial improvement in linearity results. The same conclusion sults in an absolute way. is reached by Whittier arid Gould (37) and other workers. FACTOR 2. I t is observed that a temperature rise of about However this area term is significant in comparing rate con0.3” C. occurs in the reaction mixture during a run, even at stants a t different initial concentrations due t o the different stirring speeds in excess of the upper critical rate. This maxiquantities of sucrose deposited. This correction is made in column mum is reached a t about one third life when SO= 1.16 and is in6 of Table I with the data of Figure 1 by computing the rate consufficient t o account for the initial slow period, although it constant per unit area at the half life relative to the standard run, tributes in part because of decreased supersaturation coefficient So = 1.15. With the same initial seed ratio and the tentative The subsequent fall in temperature also contributes, although to assumption that the total seed density is the same in all runs, oba small extent, to the latter falling part of the curves. viously FACTOR 3. The small grains formed during the early period will have a transitory solubility exceeding the usual value and
r’
where kso- 1.16 is the specific reaction rate constant per unit ‘reference area, and IC is the same a t a different concentration. Apparently the area term is insufficient to explain the variation of velocity with supersaturation (column 6); the ratio of velocity constants at SO= 1.06 and 1.2 is about 1/6. By actual count the ratio of the seed density in the two cases at the half life is about 1/1.5; with the plunger type of stirring it becomes much less but is still insufficient to explain the wide variation. Apparently some factor other than nucleation, such as suggested in factor 5 above, is operating. I n this situation the velocity quation, as developed later, becomes
in place of
--dS’ =
dt
k (S’
- 1)
TABLE I. VELOCITY CONSTANTS
itv
SO
SA
1.04 1.06 1.08
1.14 1.215 1.25 1.10 1.41 1.11 1.47 1.125 1.55 1.72 1.15 1.175 1.91 2.14 1.20 2.59 1.25
* kobavd.
=
dgnstant/ kobevd. Unit k o b a v d . * k. S a_ u ._ Area
A f ~ , g
0 68 0 75 0 81 0.88 0.91 0.96 1 .oo
1.13 1.20
1.38
log
0.168 0.33 0.488 0.700 1.15 1.43 1.70 2.10 2.50 4.01
0.10 0.19 0.29 0.41 0.68 0.84 1 .oo
1.24 1.50 2.36
-nn n x . no
0.15 0.25 0.36 0.46 0.75 0.88 1.00 1.10 1.25 1.70
k‘ 0.32 0.54 0.68 0.70 0.97 0.97 1 1.0 1.08 1.21
k’ b y Graphic Integra-
k ‘ , Ex. cem
tion 0.38 0.53
0.91
0.70
1.09
.. . . 0.93 .
I
.
.
1
.... ....
1.32
xxxx
....
...
1.02
... 1.0 ...
1.10
November, 1944
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
hance will inhibit the obwrvtd rate of crystallization until they grow to effective planar size. FACTOR 4. Freshly formed surfaces age rapidly ( I d ) , and as a result of this agglomeration a diminishing area is available for further growth which thus reduces the observed velocity con&ant. Ostwald "ripening" (12) may be significant. A surface active agent (0.2y0 Aerosol OT) seems t o sustain the initial rate of growth for a longer reaction time, perhaps as a result of its (iisperkng action. FACTOI~ 5. Diminishing activity of sucrose in less concentrated aolutions may account for part of the fall in this sertion of tile curves, especially a t higher init(ia1supersaturations.
LWS
a
2
fB
4BSOLUTE VELOCITY OF SUCROSE CRYSTALLIZATION
Most of the published data on the rate of crystallization of Yucrose is for seeded solutions, simulating production conditions, and presumably the effect of spontaneous nucleation is negligiblo. The most extensive and consistent data on the growth of single sucrose rrystals from pure sugar solutions is that of Kucharenko and co-workers (13) and is represented in comprsssed form in Figure 4 (left). Results of other workers (g, 21) confirm the general nature and relative values of these curves; while additional work is available (1.6,26,28,34), it is not useful for the analysis presented because of inconsistent values, inconvenient units, questionable purity, etc. Although the data selected may be approximated by a family of double straight lines up to the limit of concentration represented, it is unsuited in this form for kinetic interpretation. Some form of molecular concentration (weight ratio of sugar t o water, molality, or mole fractiQn) is preferred; and therefore Kucharenko's data are presented in Figure 4 (right) as supersaturation in terms of grams of sugar per 100 grams of water. The lines are placed with a slope of 1 and suggest a limiting monomolecular mechanism in terms of this ratio of supersaturation, with some factor operating to accelerate this growth at higher supersaturations and temperatures. Two possibilities are obvious: (A) increased nucleation and induced grain at higher supersaturation and temperature, and (B) increased sctivity in the crystallizing potential of sucrose. Suggestion A may be rejected inimediately since Kucharenko's technique consisted in the measurement of single, growingcrystals. Concerning suggestion B, it is not unreasonable t o expect that the effective concentration of crystallizable sucrose in solution may be different from its true weight concentration as a result of hydration effects (18)and/or the variety of isomeric alterations possible of the sucrose molecule (6,7). Orth (22)reviews the literature on this subject and explains the apparent acceleration of the growth velocity of sugar as the result of a favorable shift of the equilibrium: *sucrose (solution) # &sucrose (crystallizable) From boiling point data Orth calculates the effective molecular weight of the crystallizable form of sucrose to be 228; the above equilibrium may then be represented as
e
In view of the recognized limitations of boiling point determinations (9, l y ) , the preceding representation is somewhat uncertain. The activity is a superior function representing alterations in the form and concentration of crystallizable sucrose, and is independent of any specific molecular form of the modification under consideration. A variety of methods have been employed to evaluate the' activity of sucrose in dilute aqueous solution. A t ordinary temperatures and low concentrations the results of different workers are in agreement, but at concentrations approaching or exceeding saturation and temperatures above 30' C. few data are available. Values of the activity coefficient of
1
Figure 5.
QctivttyCoefficients of Suamqe in Aqueoira Solution Oo
C., Smith and S m i t h (27).
A 25' C., Soatchard (25), Robineon et al. (84). 70' C..Perman (23). Landolt-Bometein (15).
rlucrose computed from some available data are presented as log y us. molality in Figure 5. If the apparent intercept of the 70' C. curve is ignored, these three curves may be represented approximately by the empirical equations:
-
0" C. : log y = 0.101 m 25" C. : log 7 = 0.079 m 7 0.055 m
70' C. :log
The coefficients of the above equations are approximately linear in reciprocal absolute temperature, according t o the GibbsHelmholtz equation; this fact suggests that the activity coefficients of sucrose solutions up t o saturation and a t temperatures of 0 70' C. may be represented by equations of the type:
-
log
b
0
7 = bm -0.122 60/T
+
I t is not unreasonable to assume (3@)that these relations extend into the supersaturated region. By means of them, the activity of sucrose in the concentration ranges of intermt for the crystallization of sucrose was estimated, and the suggestion tested that the velocity of growth is monomolecular in terms of the supersaturation expreswd as activities or effective concentrations: Vel. = k p (a
- ~~,~td.)
This same kind of expression is suggested by an activated complex interpretation (9) of the mechanism of growth; i.e., in the equilibrium sucrose complex:
Kf
=
alu.raae =
.yauoroao mauorme
aaomgiex
Yoomplex maomDiex
If yaOmD~= is effectively constant, this expression, when formulated more properly in terms of supersaturations, is identical with the preceding form. The computed values are presented as points in Figure 6, and the line is drawn with a slope of one corresponding to a monomolecular growth. The agreement is gratifying, considering the different sources of data used and the extended assumptions required t o apply them t o the range of interest. The same conclusion obtains from direct consideration of the r w e s of Figure4; Le., in terms of activities, Vel.
-
ko (a
- a),
INDUSTRIAL AND ENGINEERING CHEMISTRY
1046 whereas on a molal basis, Vel. =
kobavd.( m
- mi)
Since the velocity is the same in both descriptions, kvbsvd.
-
ko
ym m
- ?*ma - m.
If y is not too different from ya,this approximates as kobavd.
+ -
ko
= y
k0
or log kobsvd = bm
The deviations from linearity of the curves of Figure 4 (right) are of this form. T o analyze the individual runs of Figure 1 according to this activity formulation, the equation
-dtdm = k(a - asntd.) -
Vel. =
must be integrated. The solution is a complicated type of gamma function, and for the present purpose it is advantageous to integrate graphically. The equation is restated in the form,
where S' = m/mlatd. a = ym = meb" Then: k = Js"(S - Ysatd. )dS
+
t
An area term should be inserted in the expression under the integral sign; but in view of the previous remarks regarding nucleation and for not too extended reaction life, this factor may be applied, as before, as Atl/p/Af/I" 1"1, The results of such calculations are presented as relative values in column 8, Table I, and are of the same order of value and significance as those in column 7. These computations are especially significant since they extend the application of the analysis beyond the range of Kucharenko's concentration limit of SO= 1.10 into the higher concentration range. It would be interesting to extend
.5 fi \ fi
1000
5d E
B
*a$
100
, 10
1.0
"'*, (a
-
IO a8.d.) ~~
Figure 6. Velocity US. Activity Potential
Vol. 36, No. 11
the comparison of theory and observation still further, but more quantitative information about the graining mechanism must firat be available. An additional test of this activity interpretation which is free from the manifold area-correction terms is possible with data of runs performed with a large excess of finely divided seeds (1/5 of xxxx powder). I n this case the induction period is absent and the observed velocity applies at the commencement of the crystallization when the area term is common at different initial concentrations. The results on an activity basis are given in column 9, Table I. As mentioned previously, the evaluation of the absolute crystallization velocity from experiments involving many small crystals is somewhat uncertain on account of the difficulty of determining this surface. Nevertheless this was attempted microscopically, by settling, and by dye adsorption. By the first method an average area of 0.12 X lO-'sq. cm. per seed was estimated for the crystals at the half life of the reaction whose initial supersaturation was 1.08. By settling ($5)' an average sq. cm. per seed was realized; dye adsorp value of 0.10 X tion was unsuccessful. The velocity of growth corresponding to the former value is 2700 mg. per square meter per minute which compares well with Kucharenko's value of 2000 at these conditions. Better agreement was realized by computation from a run without stirring a t SO= 1.035 with a large excess of very h e , graded seeds. The value of 1000 mg. per square inch per minute in comparison with Kucharenko's value of 755, was obtained. The search will be continued for a suitable dye method, despite the fact that i t is generally unsuitable for the evaluation of absoIute specific surface, since relative values would be fruitful in the interpretation of the nucleation process. TEMPERATURE COEFFICIENT O F CRYSTALLIZATION
The Arrhenius equation, k = e - E / R T , suggests a semilogarithmic representation, such as Figure 7, for the temperaturevelocity constant relation. On this plot values of the velocity constant relative to the value a t 30" C. are plotted according to the relation,
arid the slope is determinative of activation energy E. The curve is drawn only through points 0 and 0 rather than through the points in terms of activities, since the former are more significant for the subsequent discussion. The curve indicates a 10" C. temperature coefficient which increases rapidly a t lower temperatures from-an apparently limiting value of k w o . / k w c. = 1.54. Similar high coefficients are realized from most of the rate values reported by McGinnis, Moore, and Alston (19) for a low-purity fillmass. If one applies the not irrevocable criterion that temperature coefficients below 1.5 indicate the controlling operation of a physical process such as diffusion (SO), then the crystallization process represented in Figure 7 is not regulated by such a factor, since only above 60' C. does the slope of the curve approach such a value. While the data available on the temperature index of the diffusion coefficient of sucrose into water (15) conform with the criterion stipulated, there are indications in these and additional data (10,39) that this index may increase to a value much greater than 1.5 at the supersaturation concentrations of interest in the case of crystallization. The rapid increase of the corresponding temperature coefficient of viscosity (16, 19) in supersaturated solutions strengthens this suggestion. If, however, one computes the temperature index of viscosity of sucrose solutions a t constant degree of supersaturation at the varying temperatures (it would seem that such a variable would be more significant than a constant weight concentration In the interpretation of the mechanism of crystallization), then theresult isa value below 1.3 for the
INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1944 10
Extended observations on the effect of etirring rates on the velocity constant c o n k the suggestion that diffusion ie more rapid than growth and, therefore, is not rate determining. The previous approximate linear relation between the two variables, which is expected for a diffusion-controlling mechanism (IO), is based on observations of relatively large seeds (FJeurs6) (40-60 mesh). The effect, as already intimated, may Whit& and Gould D D e Vriea 0 be largely one of increased seeding surface as the result of the grinding action of the propeller blades. I One would expect this action t o be less pronounced with smaller seed material; it is observed that with seeds finer than 270 mesh there is no appreciable difference in the velocity constants at stirring speeds ranging from 0 (directly on the refractometer prism, or in bulk with mixing only before sampling) to 640 r.p.m. 0
I
”\ 1.0
u
h
1047
Figure 7. T e m p e r a t u r e Coefficient of Velocity Constant ThL work: O S = 1.15 Kueharenkot A S 1.02, X.So 1.05; 0 So 1.10 (Figure 4); V So = 1.10
-
-
e .
LITERATURE CITED
Nishiawa, J. SOC.Chem.I d . Japan, 39, Suppl. Binding 263-7 (1936). (2) Breedwall, C . J. F., and Waterman, H. I., Rex. trau. chim., 51, 230 (1932). (3) Browne, C.A., and Zerban, F. W., Handbook of Sugar Analysis, 3rd ed., 1941. (4) Dubourg, J., and Saunier, R., Bull. aoc. chim., 6, 1196 (1939). (6) Enders and Sigurdson, NaturwMaenschofta, 31, 92-3 (1943). (6) Fouguet, compt. rend., 150, 280 (1910). (7) Gilman, “Organic Chemistry”, 1938. (8) Ginneken, Pr J. H. van, and Smit, M. J., Chsm. Weekblad, 6,1210 (1919). (9) Glasstone, Laidler, and Eyring, “Rate Processes”, 1941. (10)Hixson, A. W., IND. ENO.CHEM.,36,488 (1944). (1 1) Jenkins, J. D.,J. Am. Chem.Soc., 47,903(1926). (12) Kolthoff, I. M., and Stenger, V. A,, “Volumetric Analysis”,Vol. I, 1 42. (13) Kucharenko, I. A., lanter Sugar Mfr., 75, MayJune, 1928. (14) Kurilenko, D. D.,Khim. Referat. Zhur., 4,No. 2,9 (1941). (1) Aniagasa and
0.1
0.01
I
I
I
-40
k
Landolt and Bornstein, PhysikalischChemische Tabellen. (16) Landt, Centr. Zuckerind., 44, 102 (1936). (17) Lewis and Randall, “Thermodynamics”, 1923. (18) McBdn, J . Phya. Chem., 33, 1800 (1929). ENO. (19) McGinnis, R. A., Moore, S., Jr., and Alston, P. W.,IND. CEEM.,34, 171 (1942). (20) Mertens, A., I V C w . intern. tech. chim. id.am.Bnrzellea, 2, (16)
complete temperature range. This again suggests that the controlling step is not a simple physical process. This conclusion corroborates the circumstance that the viscosity factor has never been satisfactorily included, and is apparently only a secondary factor, in the velocity equations of crystallizing sucrose (4, 12, $1, 99). I n terms of activation energy, values of 6500 t o 22,000 calories per mole are estimated from Figure 7 at high and low temperatures, respectively. A similar analysis of the crude data available on the rate of nucleation of sucrose sirups indicates that diffusion may very well (38) control this initial act in the spontaneous growth of a complete sucrose crystal. The incomplete data of van Ginneken and Smit (8) roughly confirma a unimolecular mechanism for the formation of sucrose crystals in supersaturated sirups. Application of this conclusion t o the data of Fouquet (6), with the specification that a definite minimum number of nuclei are necessary for identification in a n arbitrary time, leads to relative values of the specific reaction rate constant; when plotted these values give a fairly straight line with a slope corresponding to a n activation energy of about 3OOO calories per mole. The results with gum acacia and invert sugar (page 1048) increase and decreaae the viscosity (8),respectively, yet have no effect or a decelerating effect, respectively, on the velocity of crystailization. A complete examination of the diffusivity of sucrose at high concentrations would decide whether the controlling step in the crystallisstion might be a n ordinary physical process or an “activated” one.
66 (1935). (21) Nees, A. R.,and Hungerford, E. H.,private communication: IND. ENQ.CHEIM., 28,893 (1936). (22) Orth, P., Bull. a8aoc. chim. auc. dist., 29,137 (1912). (23) Perman, E.D., Tram. Faraday SOC.,24,330(1928). (24) Robinson, Smith and Smith, Ibid., 38,03-70 (1942). (26) Scatchard, Hamer, and Wood, J. Am. C h m . Soc., 60, 3066 (1938). (26) Silin, P. M., Bull. aaaoc. chim., 52,266 (1935). (27) Smith, E. R. B., and Smith, P. K., J . Bio2. Chm., 117, 209 (1937). SmolBniki, K,, and Zelasny, A., Gaz. CukrowniucC, 74, 303 (1934). Taimni, J . Phya. Chem., 33, 62 (1929). Taylor, H. S.,“Treatise on Physical Chemistry”, 2nd ed., 1932: Moelwyn-Hughes, “Reactions in Solutions”, p. 278, 1933. Thieme, J, Q., Arch. Suikarind., 41, 17 (1938). Van Hook, Andrew, J . Phy8. C h . ,41,693 (1937). Volmer, “Kinetik der Phasenbildung”, 1939. Vries, a. H. de, Arch. Suikerind. Nedstland en Ned.-Indii, 2,67 (1941). (36) Wagner, L. A., Proe. Am. SOC.Tseting Materiala, 33, 11, 668 (1933). (36) Webre, A. L.,Proc. 11th Ann. Conf. AESOC. teonicos uucareroa Cuba, 1937,9-16. (37) Whittier, E. D.,and Gould, 8. P., IND.EHQ.CHEM., 23, 070 (1931). (38) Young, S. W., and Van Sicklen, W. J., J. Am. Chem. SOC..35, 1007 (1913). (39) Zuber. R.,Z . Physik, 79,280 (1932).
